No worries. I just used the mesh because it was a larger hole and that really helped to have a stable base for applying thinner smoother layers.

Personally if it was me? I'd just try and sand it as flat as possible, see if I could get it flat. You might need a rougher grade of sandpaper and a sanding block if it's slow going. Then smooth it with finer. Then paint the spot in a few thin layers drying in between - if it's still looking very obvious you might then choose to paint the whole door.

I'm not a professional though. Just a renter that had to do this a couple of times